DETERMINATION OF BOUNDARY ENERGIES OF Cu FROM THE SHAPE OF BOUNDARY SiO2 PARTICLES

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DETERMINATION OF BOUNDARY ENERGIES OF Cu FROM THE SHAPE OF BOUNDARY SiO2

PARTICLES

H. Miura, M. Kato, T. Mori

To cite this version:

H. Miura, M. Kato, T. Mori. DETERMINATION OF BOUNDARY ENERGIES OF Cu FROM

THE SHAPE OF BOUNDARY SiO2 PARTICLES. Journal de Physique Colloques, 1990, 51 (C1),

pp.C1-263-C1-268. �10.1051/jphyscol:1990141�. �jpa-00230299�

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COLLOQUE DE PHYSIQUE

C o l l o q u e Cl, s u p p l k m e ~ . t au n o l , T o m e 51, janvier 1990

DETERMINATION OF BOUNDARY ENERGIES OF Cu FROM THE SHAPE OF BOUNDARY SiO, PARTICLES

H . MIURA, M . KATO and T . MORI

Department of Materials Science dand Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan

Abstract

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The boundary energies of symmetric [Oil] tilt and [Oil] and [001] twist boundaries of Cu were measured by a new method: Si02 particles were introduced on grain boundaries by internally oxidizing bicrystals of Cu-0.06XSi. The boundary energies in terms of the Cu-SiO2 interfacial energy were determined from the lenticular shapes of boundary Si02 particles observed by transmission electron microscopy.

Besides the energy cusps reported previously for FCC metals, several new cusps were clearly resolved by the present method: 127, 11, 33 and 57 for [Oil] twist and W1 and 29 for [OOl] twist boundaries. The relative boundary energy was found to depend sensitively on the partial pressure of oxygen, as-oxidized or degassed. That is, oxygen segregates on boundaries, affecting the boundary energies.

1 - INTRODUCTION

It is generally accepted that the energies of grain boundaries play a central role in some phenomena associated with boundaries: fracture strength, boundary corrosion, boundary precipitation, the preference of particular boundaries in recrystallization and grain growth, etcll-41. Besides the work which attempted to examine-boundary energies in terms of arrays of dislocations/5/, many data of boundary energies have been accumulated so that other properties or phenomena involving boundaries can be discussed in correlation with the boundary energies.

Most of the important data of the energies of well-characterized boundaries are documented in an overview by Sutton and Balluffi/6/.

Two methods have been traditionally employed to determine the energies of boundaries:

surface groove and triple junction methods. These methods have some drawbacks in accurate measurements. It appears inhibitingly difficult to accurately measure the dihedral angle between two free surfaces in the surface groove method. This is particularly so at the very tip where a boundary emerges at a surface. There is also a case where a boundary consists of microscopically zig-zag facets which have lower energies than the boundary to be examined. An example of such a case will be given later. Although sufficient accuracy may be maintained in the measurement of dihedral angles in the triple junction method, this method also involves an uncertainty: the proper assignment of the so-called torque terms/7/ which are known only after the complete determination of the energies of boundaries with every possible orientations.

The present study employed a new technique in the determination of boundary energies in Cu. Although the applicability of the technique was suggested earlier/8/, the technique has not been used in a systematic manner until now and, thus, will be described below. Introduce a Si02 particle on a grain boundary of Cu by an adequate method. It is known that a Si02 particle i s spherical inside a Cu grain after sufficient time of annealing at high temperatures/8/. Such in-grain spherical particles are seen in Fig. 1. This means that the interfacial energy between Cu and Si02 does not depend on the orientation of a Cu-Si02 interface and is isotropic. Under this condition, it can be shown that a Si02 particle on a boundary takes a lenticular shape bounded by two truncated spherical surfaces, as shown by the inset in Fig. 1, after the equilibrium (energy minimum) is attained. The boundary plane forms

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990141

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Cl-264 COLLOQUE DE PHYSIQUE

Fig. 1

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Si02 particles on (a) C11 {311]{311) and (b) C9 {122){122) boundaries. The scale bars are 0.5~1. In-grain particles are also seen.

the mirror plane of symmetry. a, half the dihedral angle of the equilibrium lenticular shape, is given by

where y~ is the energy of the boundary between two abutting grains and y1 the interfacial energy between Cu and Si02. Thus, by measuring a of the lenticular shape of a boundary Si02 particle, we can determine the relative boundary energy, m/yI. The direct application of Eq.

(1) requires the determination of a, the measurement which may involve a certain degree of inaccuracy. However, this ap arent drawback can be overcome: simple geometrical consideration leads to cosa=(aq-b2)/(a2+b2), where a is the diameter of the SiO2 particle on the boundary and b the distance between the two apexes of the lenticular shaped particle, as shown in Fig. 1. Thus, Eq. (1) is rewritten as

It is obvious that the measurement of a and b involves less uncertainty. The actual determination of the shape of boundary Si02 particles was made after the spherical shape of in-grain Si02 was confirmed. This was to ensure that sufficient time had been allowed for diffusion of Cu and the constituents of SiO2 to attain the equilibrium.

The isotropy of the interfacial energy of Cu-Si02 eliminates an unknown role of the torque terms in the calculation of boundary energies. Besides this advantage, the present method is free of ambiguity that occurs in a boundary which might consist of facets but looks macroscopically flat. By the present method, we can always ascertain that the boundary whose energy is measured is straight in a microscopic scale. An example of a boundary with facets will be given later.

In the present study, we have measured the energies of symmetric [Oil] tilt and [Oil] and [001] twist boundaries in Cu, using the above mentioned method. We have also found that the presence of small amounts of an impurity (oxygen)in the bulk changes the energy of a boundary.

2

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EXPERIMENTAL

Bicrystals, 2mm thick, of Cu-O.OG%Si having symmetric [Oil] tilt, [Oll] twist and [001]

twist boundaries were grown by the Bridgman method in graphite molds, using seeds. After annealing at 1273K, the bicrystals were internally oxidized at 12733 for 24hr by the pack method with a mixture of Cu, Cu2O and A1203 powders. They were further degassed at 1273K for 24hr in vacuum on a graphite mold for standard measurements. The effect of degassing will be mentioned later. The shape of Si02 particles formed by these treatments was examined by transmission electron microscopy (200kV). Thin foils, containing grain boundaries, for this observation were prepared by mechanical polishing and jet polishing in an electrolyte of H20 and H3P04. For each boundary, more than fifteen particles were observed in the orientation where the grain boundary was always parallel to the incident electron beam. The relative

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Misorientation Angle ( deg.

Fig. 2 - Relative boundary energy against misorientation angle for symmetric [Oil] tilt boundaries of Cu. Relative boundary energy is higher after oxidation (the dotted curve) than that with an additional degassing treatment (the solid curve).

boundary energies were calculated from the observed shapes of Si02 particles with Eq. (2). In some cases, Si02 particles on a boundary were observed from two directions, approximately 90"

from each other, to ensure that the particles had mirror symmetry lenticular shapes. A change

"in the calculated energy in this assertion was within the standard deviation for the energy of an individual boundary.

3 - RESULTS AND DISCUSSION 3.1. Boundary energy

Examples of Si02 particles on symmetric [Oll] tilt boundaries are shown in Figs. l(a) and (b). Figure l(a) was taken from a C11 {311){311] boundary and Fig. l(b) from a C9 {122){122) boundary. The spherical shape of in-grain particles ensures that the equilibrium has been attained in a practical sense. The Si02 particles on the C9 boundary in Fig. l(b) are more oblate than that on the C11 boundary in Fig. l(a). That is, just visually examining the shape of Si02 particles, we can roughly judge the magnitude of the energy of a boundary: the energy of the C9 {122){122) boundary is larger than that of the C11 {311){311} boundary.

Figure 2 is the y(0) diagram where the energies yg of symmetric [Oll] tilt boundaries are plotted against the misorientation angle 0. The solid curve was obtained from oxidized and degassed bicrystals and the dotted curve from as-oxidized bicrystals without the degassing treatment. The effect of the degassing treatment on boundary energies will be discussed later. The general shape of the solid curve is similar to those observed for A1 by Hasson and Goux/9/ and Otsuki and Mizuno/lO/. Similar to Hasson and Goux, we were able to resolve the cusp at 0=39', C9 {122){122), in addition to the well established cusps at 0=70.5", C3 {111){111], and 0=130°, C11 {311){311}. Its existence is backed by the small scatter of data in the present study. The implication by Sutton and Balluffi[6] that a cusp exists at 0=llO0, C3 { 211) { 21 1) has not been definitely confirmed. The data point for this value is the lower bound as will be described below, but it cannot indicate the presence of a cusp without reservation.

We attempted to grow several times bicrystals with the C3 {211){211} boundaries.

However, it was found that the boundaries, macroscopically described by {211){211), always consisted of two flat facets, one inclining by 6.7' to {211) and the other by -6.7" to {211).

This observation does not coincide with the existence of the energy cusp at {211){211) for [Oll] tilt C3 boundaries as reported by Goodhew, Tan and Balluffi and Andreyeva and

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COLLOQUE DE PHYSIQUE

O;

^I

I I

15 30 45

Misorientation Angle (deg. )

Fig. 3 - Relative boundary energy against misorientation angle for [001] twist boundaries.

I I I I I I I I

0 10 20 30 40 50 60 70 80 90 Misorientation Angie (deg. )

Fig. 4

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Relative boundary energy against misorientation angle for [Oll] twist boundaries.

Fionova/ll,l2/. These facet planes were tentatively assigned to {l3 5 5){11 7 7) by referring to Vaughan/13/, who found similar boundaries in an annealed polycrystalline austenitic stainless steel. The present finding of the faceting of {211){2111 to I13 5 5)Ill 7 71 and the observation by Vaughan indicate that the {l3 5 5){11 7 7) boundary has a lower energy than the symmetric {211){211) boundary. By examining the shape of Si02 particles, the relative boundary energy of { 13 5 5){ 11 7 7) was determined 'to be 0.22. From this, the lower bound for the relative energy of C3 {211}{211) was calculated as slightly larger than 0.22. This discussion indicates an advantage in the present method of the boundary energy determination.

Figure 3 is the y(0) curve for the [001] twist boundaries. The existence of the energy cusps at 8=23O (C13), 8=28" (C17) and 0=37" (C5), as observed in A 1 by Otsuki and Mizuno/lO/, was confirmed. In addition, two more cusps at 0=13O (C41) and possibly at 0=44O (129) were found. Brokman and Balluffi expected by simulation calculations that the 0=16.3O (C25) boundary is associated with an energy cusp/14/. However, Figure 3 clearly denies such an expectation but rather indicates that the [001] twist C25 boundary with the fourth lowest C value has an energy close to that of a random boundary. In accordance with this observation, we recently found that the sliding behavior of a [001] twist C25 boundary deviates from those of other low C boundaries and is close to that of a random boundary.

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m

0.5

W

L

d

m : (011 ) t i l t 38.5 (19)

a n : (011) tilt 137.1 (E9)

: (011) tiIt129.5(111)

O ' i

²⁴^I ⁴⁸^I ⁷² ⁹⁶

Time ( hours 1

Fig. 5 - The effect of degassing and re-oxidation on relative boundary energies.

Figure 4 shows the energy of [Oil] twist boundaries against the misorientation angle. In the past, only a shallow cusp at 8=70.5O(C3) was reported for A1/10/. The cusp at 8=70.5O observed in the present study is highly asymmetric but is sharp. In addition to this, we have detected four more cusps at 8=32O (C27), 8=51° (Cll), 8=5g0 (C33) and 8=83" (157).

We will briefly discuss why we have found new cusps. Certainly, the energy is determined not only by the character of a boundary but also by a material property. The fact that most of the energy cusps found in the present study of Cu for the [Oll] tilt and [OOl] twist boundaries were also observed in A1 suggests that the former effect i s predominantly operative. I t appears that the discovery of new cusps at C29 and C41 in [001] twist boundaries and those at C27, Ell, C33 and C57 in [Oll] twist boundaries is due to better sensitivity in the present method.

3.2. Effect of degassing and re-oxidation

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Reproducibility of boundary energy

Si02 particles were formed by the pack method which produced an oxygen partial pressure of ~ 1 0 - ~ ~ a (dissociation pressure of Cu20). When Si02 particles were observed and the corresponding boundary energies were determined without a degassing treatment, we obtained the dotted curve in Fig. 2 for [Oil] tilt boundaries. It is clear that the relative boundary energies depend on the oxygen pressure under which the equilibrium state is attained. Two factors must be considered to discuss this observation. Both of them are caused by the segregation of oxygen; one on grain boundaries and the other on Cu-Si02 interfaces. It is obvious that the segregation on boundaries or interfaces changes their energies. As shown in Fig. 2 , the relative energy is higher in the as-oxidized condition than in the degassed condition. This means that either the interfacial energy of Cu-Si02 becomes smaller or the boundary energy of Cu increases by the oxygen segregation. The equilibrium oxygen segregation on the Cu-Si02 interface is determined solely by the oxygen partial pressure. Thus, if only the interfacial energy of Cu-Si02 is affected by the magnitude of the oxygen pressure, the two curves in Fig. 2 should become identical except for a multiplication factor. However, this is not necessarily the case. The clearest evidence against the supposition that only the Cu-Si02 interface has the segregation of oxygen is the feature of the energies around 8=39O (C9). In the degassed state, the 8=39O boundary has an energy cusp while in the as-oxidized state, the existence of a cusp is obscured. In short, it is our contention that the segregation of oxygen occurs in Cu grain boundaries and increases their energies. It is very likely that the amount of oxygen segregation on a grain boundary and the corresponding increase in its energy depend on the character of the boundary.

Next, we will show that the relative boundary energies given in Figs. 2 to 4 can be taken as the equilibrium values in their respective conditions, degassed or oxidized, for all practial purposes. We will further show that these values are reproduced reversibly in the degassing or oxidizing condition when sufficient time is allowed for the achievement of equilibrium by diffusion.

In Fig. 5, the relative boundary energies, determined by the shape of Si02 particles, are

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Cl-268 COLLOQUE DE PHYSIQUE

plotted against degassing or oxidation time at 1273K for three symmetric [Oll] tilt boundaries; 0=39O, 130° and 137O. The foils for this observation were taken from the center of 2mm thick samples. As seen here, the relative boundary energies decrease rapidly in the early stage of degassing and later saturated to almost constant values after 24hr degassing.

This observation assures that the 24hr degassing employed in the standard measurement of boundary energies is sufficiently long. After 48hr degassing, 2mm thick samples were again oxidized at 1273K by the pack method and the relative boundary energies were measured using foils taken from the center of the samples. It is seen that the relative boundary energies increase rapidly to approach the values determined in the as-oxidized state. These observations indicate that the present method to determine the boundary energies is sufficiently sensitive to reflect the state of boundaries. Figure 5 also shows that the second degassing decreases the energies to the value obtained by the first degassing.

Whichever dominantly affects the relative boundary energy, the segregation of oxygen on a Cu boundary or a Cu-Si02 interface, the above observations show that a change in the boundary or interfacial energy by the oxygen segregation can be detected reproducibly. Although the elimination of oxygen segregation cannot be completely claimed in the present degassing treatment, the energy determined after degassing should be closer to the intrinsic value.

Utilizing this change of the shape of Si02 particles on boundaries by degassing or re- oxidatipn, we can possibly estimate the diffusivity of oxygen along grain boundaries. We can also examine the dependence of oxygen diffusivity on the character of boundaries. These subjects will be reported in a separate paper.

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SUMMARY

After introducing Si02 particles on boundaries of bicrystals of Cu by internally oxidizing Cu-Si, the shapes of the particles were observed by transmission electron microscopy. From the shape of the particles, the boundary energy relative to that of the Cu- Si02 interface was determined. The results obtained were as follows:

(1) Symmetric [Oil] tilt boundaries have energy minima at 0=39O (C9), 0=70.5 (13) and 8=130°

(111) (0 is the misorientation angle), as reported previously in other FCC metals.

(2) Besides 0=70.5' (13), the 0=32O (127), 8=51° (Ell), 8=59' (133) and 0=83' (157) [Oil]

twist boundaries have energy minima.

(3) New energy cusps were found at 8=13' (141) and 8=43O (129) in [001] twist boundaries.

(4) Degassing treatments reduced the relative boundary energies from the as-oxidized state.

Re-oxidation treatments increased the energies back to those in the as-oxidized state. This finding means that oxygen segregates on boundaries and affects boundary energies.

Acknowledgement

This research was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 63550533).

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